Contents

Before

My most recent math class was linear algebra, so right now, vectors, vector spaces, and matrices come to mind when I think of mathematics.

Do you consider yourself a mathematician?

I do. I use math every day in class and in my life. I ask the same questions that other mathematicians have asked for years. Without the ability to count and manipulate numbers and variables my life would be a mess.

When you hear the term biology, what comes to mind?

I visualize many things when I hear the term biology. Sometimes I think of plants and animals. Other times I can see DNA coils winding and unwinding (probably the result of being force-fed the central dogma of biology for the last 8 years in school).

Do you consider yourself a biologist?

I do. I have had so much biology in my education and now I am taking that education and giving back through my research on instability in cardiac myocytes. I also do not plan to cease learning more biology in the future; we live in an ever changing world where there is new biology every day waiting to be observed, quantified, or tested upon.

After

What did you find most interesting about the Stewart reading?

I enjoyed the description of a rainbow. I have never heard anything like it, I had no idea that rainbows were personal. Optics is a really interesting field of study, and rainbows are an excellent example of natural optics at it's finest. Of course this was a great example of how math is important, none of Stewart's description would have been possible without math.

What did you find most interesting about the Janovy reading?

I have never really thought of the importance of studying something as seemingly unimportant as frogs, but Janovy makes a good argument for studying any part of our Mother Earth. If we really are this new species that Janovy says we are, then not studying the other species around us who have been here far longer would be a huge mistake. The reading gave importance to studying really anything, and I liked that. I am doing research with probabilistic cellular automata and studying the human heart. And I always felt that I needed to be studying some direct human phenomena, so this article is almost humbling, and a reality check. We are such an insignificant part of Earth and yet we have the capabilities to destroy it (and sadly we take advantage of these capabilities to the maximum).

What does it mean to be a biologist? Do you consider yourself a biologist?

Being a biologist is not just studying, observing and testing natural phenomena. It is not enough to be up to date on the latest material or memorize the processes that go on in living organisms. Being a biologist means seeing the connections between all living things in this world. The idea that we are all interconnected is key to biologists, and key to us understanding our world which should be more of a priority in society than it is. I do consider myself a biologist. I care about our earth and educate myself on everything in my grasp. I want to learn more for my own fascination and so I can help others learn about our environment and how we can protect it. I love nature and would hate to see it destroyed forever.

What does it mean to be a mathematician? Do you consider yourself a mathematician?

Being a mathematician is not just plugging in numbers and solving equations. It is seeing the math in nature, technology, and life. Everywhere we look there is math. And all phenomena in nature can be described mathematically. We learn the math behind nature so we can recognize patterns and come to understand how it relates to us. If we want to survive as a species and preserve nature then we need to be able to recognize the patterns of nature and see the similarities between ourselves and other species. I am a mathematician not only because I love math and practice it every day but because I see it in everything I do and appreciate what a powerful tool math is.

What are the similarities and differences between the two readings?

Well for one thing, they are both about severely misunderstood subjects of study. Or maybe not even subjects of study, but ways of life. People see math as numbers and equations, the Stewart reading points out this fact and that everything has math in it, but it works in the background. If math were blatant in all areas it is used we would be overwhelmed. The study of a frog seems so insignificant in our world today where money and power are everything. The more you have the more successful you are in life as a person. Society values monetary success over all and looks over biology or takes it for granted. Treats it like it is something that will be there forever, and as if we know everything there is to know about it. Well we have but merely scratched the surface, the vast majority of biology will go undiscovered and disappear into extinction long before we understand it. It is sad that people today cannot understand the value in studying a frog or some other species. And there are many people out there who do not know that they are biologists, they are too blinded by money to recognize it. Both readings also give the perspective of someone who made the choice to become a mathematician or biologist, of someone looking back on their life and knowing that they made the right career and life choice. They both also tell that technology has benefitted mathematics and biology, in math, providing opportunity for more math (as all technology involves math), and in biology, by giving biologists the tools necessary to study nature.
The readings differ as well. The Stewart reading seems to be reassuring Meg that there is money in mathematics, so it is not something to be worried about. While the Janovy reading seems to bash any pursuit of monetary gain in place of becoming a biologist. Janovy does not really give hope to someone looking for financial benefit, maybe trying to attract those hardcore enough to study biology with no worry of money. The Stewart reading also stresses that seeing math in everyday life is easier than most people think, while the Janovy reading stresses more the importance of the seemingly unimportant biology or nature that we see blatantly in front of us everyday (it's pretty easy to go outside and look at your front lawn i.e. nature).

Before reading the Stewart chapters (on your honor), answer the following questions; When you hear the term mathematics, what comes to mind? Mathematics is a discipline that encompasses numbers, logic, equations, and theories. In my experience, math is a highly conceptual topic of study. Math requires learning how to reason and the methods one needs to reach an answer (or answers). Consequently, it is this process of reasoning that I find the most valuable in the field of mathematics in regards to my everyday life.

Do you consider yourself a mathematician? why or why not? I would consider myself a mathematician on a very basic level because I use math in other disciplines, such as physics, chemistry, and biology. All other science fields require a general knowledge on math concepts (e.g. probability, statistics, algebra, derivatives, etc.). I do not consider myself a highly skilled mathematician because I simply have not taken many math courses, and I do not have much knowledge on the subject.

Before reading the Janovy chapter (on your honor), answer the following questions; When you hear the term biology, what comes to mind? I think of all forms of life and everything that explains it. Biology is a study that embodies a broad range of topics including plants and animals, and the mechanisms by which they grow and develop. When I hear the term biology, I also think about how all living things relate to one another and the many comparisons scientists can draw between the different aspects of biology.

Do you consider yourself a biologist? why or why not? I consider myself a biologist not only because it is my major, but also because I feel like I am constantly thinking about different aspects of biology. I am always curious about why certain things are the way they are, and most times I try to find the explanation to these questions. To be a biologist, in my perspective, is to have this interest on gaining new knowledge on different aspects of life.

After reading the Stewart and Janovy chapters, answer the following questions:

What did you find most interesting or provocative about the Stewart reading? The most interesting I found about the Stewart reading was all the examples he used in relating the study of mathematics to everyday life. In the previous question of "What do I think about when I hear the term math?" I discussed how mathematics is a study that can be applied to the other sciences. However, Stewart points out that math can be applied to the world outside of science. He gives examples such as GPS, plane flights, the Internet, modes of communication (e.g. cell phones), genetics, GMO crops, rainbows, and even animal movement. All these examples represent only a minute fraction of how math is applied in daily life. The most interesting example was when Stewart related the lattice structure of a crystal to the position of birds in a given area.

What did you find most interesting or provocative about the Janovy reading? Janovy's argument on paradigms in biology is one that I found to be interesting. Janovy introduces this topic when discussing Thomas Kuhn, who defines what a paradigm is. Paradigms in biology are areas of study that are the most widely accepted. Janovy argues that "paradigms both direct and limit intellectual development" (Janovy 11). Later in his paper, Janovy gives an example of how scientists will apply for grants , often times with a statement of objective that leans towards the aim of the corporation. It is interesting to me that I notice this in today's society. There is a strong emphasis on the study of genetics in comparison to decades ago. This paradigm has influenced not only biologists, but also technicians and physicians as well. Another aspect of the Janovy reading that I found interesting was Janovy's theme of evolution throughout the chapter. He states that any scientist can relate their field of study to evolution (5). In his conclusion, Janovy ends with a comment on how biologists today have become so specialized in their work; however, it is this specialization that will drive one to "role extinction." The basis of biology, however, is to instead broaden one's view, exactly like the naturalist.

What does it mean to be a biologist? Do you consider yourself a biologist? Why or why not? What I find interesting about the Janovy reading is both the similarities and differences he makes between biologists and nonbiologists. An early biologist, which one can think of as a naturalist, would consider humans as just another species in the existence of the biosphere. In contrast, the rest of the public community tends to focus on a culture centered on humans. Janovy argues that a biologist should continue naturalist ideals. He uses individuals such as Thomas Hunt Morgan, Jacques Monod, and Charles Darwin to exemplify how successful biologists were attached to the world of living organisms since an early age (Janovy 6). Having an interest in the natural world is only one aspect of what it means to be a biologist. Janovy continues to discuss how biologists perceive their surroundings. He contends that biologists see complexity through uniformity, they tend to pose questions, and they also sense interdependencies in the environment around them (19). Janovy also discusses the attributes of a modern-day biologist. Since World War II, technological advances have become intertwined into the field of biology. Today, biologists use tools; however, they tend to not uphold the values and world views of a naturalist. The study of biology requires a knowledge on computers and math in order to reach biological conclusions. Janovy clarifies his argument by discussing how biology has become interdisciplinary-- relying on other sciences such as chemistry, physics, mathematics, and even the social sciences. Although these are descriptions of the present-day biologist, Janovy concludes that biologists need to not stray away from the original values and worldviews of a naturalist.

After reading the Janovy reading, I still consider myself a biologist. Like Morgan, Monod, and Darwin, I found myself interested in living organisms since a young age. Although I have learned and performed various technological methods to determine biological conclusions, I still value and revel in nature, which is what Janovy considers to be a vital attribute of a biologist. I try to surround myself with the natural environment at every opportunity.

What does it mean to be a mathematician? Do you consider yourself a mathematician? Why or why not? In the Stewart reading, a mathematician is one that can not only see patterns in various settings, but is one who can mathematically justify why these patterns occur. For example, Stewart is able to relate an atom's crystal lattice structure to bird positions, and he can even mathematically deduce why rainbows exist.

After reading the Stewart reading, I still do not consider myself an actual mathematician. Stewart is an individual who bridges the gap between mathematics and nature. In contrast, I do not see patterns in the environment to the extent that he does. For example, of course I have noticed the shape of a rainbow; however, I have never thought about the mathematical reasoning behind it. From this reading, I hope to become more aware of the significance of math in my daily life.

What are the similarities and differences between the two readings? Both readings make distinctions between how the field of study is perceived by the general public and what it actually is. In the Janovy reading, he argues that biology is understood to be a field of technological tests, drawing from other disciplines. However, the root of biology should be in the value of nature. Similarly, Stewart claims that the notion of the public on mathematics is that it is simply a field of numbers. In reality, math is responsible for many things we need on an everyday basis. In a sense, math is devalued because of its obscure role in society.

Another similarity between the two readings is that both biologists and mathematicians have a distinct way of thought that is dissimilar from other individuals. Biologists tend to think of humans as another species, whereas society puts more value on humans over other species. Similarly, Stewart contends that mathematicians think differently as well, as noted in the last paragraph of chapter 5. Mathematicians tend to see trends and patterns in their surroundings, which math can explain.

Although both readings display similarities, they are also different. Firstly, Janovy argues that most biologists lose sight of what it truly means to be a biologist, which is upholding a passion for nature and living organisms. Instead, modern-day biologists may get caught up in paradigms and other influences. In contrast, Stewart suggests that mathematicians are the only ones that understand the true meaning of math, which is the fact that math can be used in everyday life, including in nature. The public, however, is the group of individuals who have the misconceptions on the field of study. Secondly, the Janovy reading proposes that although nature and evolution are the main pillars of biology, biology today is a study which encompasses the other sciences. In contrast, Stewart poses that it is mathematics that highly contributes to other disciplines.

Before

When I think of mathematics, I think of solving problems using numbers, logic and equations. Mathematics is very intellectual and solving problems in math is almost like completing a puzzle.

Do you consider yourself a mathematician? Why or why not?

I do not really consider myself a mathematician. To me a mathematician is someone who has studied a lot of math and has a solid understanding of many the concepts. I do not think I have a great knowledge when it comes to math. Although I do use some math in my everyday life, it is simple and not to the level of someone who I would think of as a mathematician.

When you hear the term biology, what comes to mind?

I immediately think of all the living things in the world around us. I think of plants, animals and microorganisms. For me the biggest thing that comes to mind is the human body. I have always been interested in the human body. I often think about how it is composed and how we function on a daily basis.

Do you consider yourself a biologist? Why or why not?

I do consider myself a biologist. I have always been interested in biology from a young age and I have been learning about it for as long as I can remember. I think that I have amassed a lot of knowledge when it comes to biology. I find that biology is one subject that I always want to know more about. I know that advances in biology are constantly being made and this keeps me interested to continue learning.

After

What did you find most interesting or provocative about the Stewart reading?

I found Stewart's discussion about the red stickers to be most interesting. He believes that the public has the wrong view about mathematics and he wishes that could be changed. He suggests putting a red sticker on everything that uses mathematics that says "Math Inside." He makes the point that math is in almost everything in our world today but nobody knows it or appreciates it. It was interesting to see how many examples have math in them, including vegetables. Many would not think of the math that goes into commercial breeding. I found this point to be very interesting as I have always had an interest in genetics but I have not fully thought about all the mathematical methods that go into it.

What did you find most interesting or provocative about the Janovy reading?

I found the author's story about his encounter with the woman at the high school volleyball tournament to be most interesting. He talks about discussing his work and the work of his colleague to the woman. It was interesting to see the two different perspectives they had about the conversation. Janovy thought his colleague's work was interesting and important. He knows his colleague as a well respected man who does important work for the further development of biology. It was funny to see that the woman did not exactly agree. She gave a look of disapproval when she learned that the colleague did work on frogs in South America. She does not see this work as beneficial to our society. As Janovy says, this work will not cure cancer or stop pollution, so most people may not see the benefits of the work. I liked that Janovy was able to defend his own position as biologist. He saw the work as beneficial to ultimately contribute to overall view of the world. Without research such as this our knowledge about our world will cease to grow. It was interesting to see the two different trains of thought between them.

What does it mean to be a biologist? Do you consider yourself a biologist? Why or why not?

A biologist is one who has an interest and an inherent attachment to the world of living organisms. A biologist knows and understands that each living organisms has levels and levels of complexity. They understand that there is very little understood about living things and that there is much more to learn. A biologist has the drive to continue to search for new answers and continue to learn more and more about the world around us. Biologists want to know more and hope to discover it. I still consider myself a biologist. I share a lot of the traits that Janovy discusses. I know that biology is a field where still little is known and I like that about it. I want to know more about the world around us and I look forward to learning new things about biology.

What does it mean to be a mathematician? Do you consider yourself a mathematician? Why or why not?

There is more to being a mathematician than using numbers and equations to solve math-related problems. A mathematician sees math everywhere and can use math to create many new technologies. According to Stewart, we see mathematicians around us all the time but we almost never notice. A mathematician sees mathematical patterns in their everyday life, such as noticing the spacing of birds on a wire. I still do not consider myself a mathematician. I do not often notice math in my everyday life. I have rarely noticed any type of mathematical patterns in my life or thought about how to mathematically explain a rainbow. I think I could learn to become a mathematician, but at this point I do not think the way a mathematician most often does.

What are the similarities and differences between the two readings?

Similarly, in both readings, both authors make the point that their respective field of studies are often misunderstood. The authors seem to feel that general public have misinformed opinions about their fields that are often too specific and limited. Stewart demonstrates that math is everywhere. It is not just numbers written on paper but it is the foundation of many advancements in our world today. Janovy also shows that there is more to biology than what is on the surface. When he is speaking about the frogs in the south america, most people would not see the significance of this but Janovy does. He argues that biologists appreciate these studies because they contribute to our understanding of the world. The authors believe people in their own fields of study think differently than others. A mathematician notices patterns in nature and can rationalize them mathematically. A biologist sees the importance in various studies that may not seem significant on the surface, but will contribute to our biological knowledge long term. It seems that the authors think the general public does not fully understand what they do and how important their fields of study are.

There are differences in the readings as well. One, in the Janovy reading when he tells others he is a biologist they have the impression that they do not make much money. And the author does not say much to contradict this point. In Stewart's reading, he explains that there is a ton of potential to make a lot of money as he list off some of the new, very successful technologies that were created with math. Another difference is seen tn the Janovy reading as he explains that in biology not much is known and biologists need to actively go out and look for answers. He thinks a good biologist will seek out the answers to questions about the world. Stewart seems to have a different philosophy as he explains that anyone can see math in nature and it is just a matter of noticing different patterns that can make one a mathematician. Janovy also mentions that worldviews between fields of studies seem to vary dramatically, showing that every field of study has unique ideas about the world. I think there is potential for these views to come together and complement each other, just as math can complement biology and vice versa, as they do in genetics.